I'm pretty sure I can handle a single offer-varying acceptance or confirmation of an oral contract at this point. What I'm not sure about is when there are 15 back and forth writings in the course of making a contract, which one is the acceptance?

It entirely depends on what the content of the 15 letters is. And then the terms depend on what the relationship between the parties is and what the accepting party tried to change about the contract and what kind of performance happened and you hopefully get the idea that 2-207 doesn't give you a very clear rule to apply to a generic situation.